$\dfrac{ -3s - 9t }{ -8 } = \dfrac{ -8s - 10u }{ 4 }$ Solve for $s$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -3s - 9t }{ -{8} } = \dfrac{ -8s - 10u }{ 4 }$ $-{8} \cdot \dfrac{ -3s - 9t }{ -{8} } = -{8} \cdot \dfrac{ -8s - 10u }{ 4 }$ $-3s - 9t = -{8} \cdot \dfrac { -8s - 10u }{ 4 }$ Reduce the right side. $-3s - 9t = -{8} \cdot \dfrac{ -8s - 10u }{ {4} }$ $-3s - 9t = -{2} \cdot \left( -8s - 10u \right)$ Distribute the right side $-3s - 9t = -{2} \cdot \left( -{8s} - {10u} \right)$ $-3s - 9t = {16}s + {20}u$ Combine $s$ terms on the left. $-{3s} - 9t = {16s} + 20u$ $-{19s} - 9t = 20u$ Move the $t$ term to the right. $-19s - {9t} = 20u$ $-19s = 20u + {9t}$ Isolate $s$ by dividing both sides by its coefficient. $-{19}s = 20u + 9t$ $s = \dfrac{ 20u + 9t }{ -{19} }$ Swap signs so the denominator isn't negative. $s = \dfrac{ -{20}u - {9}t }{ {19} }$